This is an interesting number puzzle:
How many ways can you tile a chessboard with dominoes (assuming each domino covers 2 squares on the chessboard)? Googling this reveals the amazing result of 12,988,816 distinct tilings.
There are 28 dominoes in a standard set, which would cover 56 squares on a chessboard, leaving 8 vacant squares. I experimented with placing the set on a board, leaving the vacant squares in random squares. I was able to generate a large amount of tilings; but the randomness of the gaps was aesthetically displeasing.
I then tried establishing the eight vacant squares first, in a symmetrically pleasing position. I was able to find 2,098,008 solutions in just over 5 minutes, using a technique know as ‘backtracking’.
Continue readingWith the current debate about the (possible) risks from Artificial Intelligence, I have been reminded of two science fiction stories I read as a young boy.
The first was ‘The Last Question’ by Isaac Asimov. I can recommend this very highly, and luckily it is currently available on the web, here. Apparently, it was his favourite short story out of all the short sf he had written. Without giving away the plot, it concerns a question asked of a computer, and the response given.
Another story I remember from my teenage years is ‘Sole Solution’ by Eric Frank Russell. I have searched for this on the net, but been unable to find a free copy; however, you should read it if you can get hold of a copy.
Both of these stories are classics of science fiction, engendering a sense of awe with the final paragraph.
The latest addition to my site is Atomic Box, a puzzle game which has been designed by me. This image is from the puzzle for Bank 1, Level 2.
A number of molecules placed in a box are moved to new positions. You have to find the possible original positions of these molecules. There are 7 types of molecule, each of these affect light beams hitting it in different ways. Details of these molecules are available on the puzzle page.
You are given 32 clues on how the light beams were affected by the original placement of the molecules and also how the current placement is affecting the same beams.
SolveX is an app on my site which can be used to search for words where some of the letters are known. The user enters the word with spaces or ‘.’ indicating the unknown letters. The app will display matching words.
It can also be used to search for anagams. To find anagrams the user can enter some text and the app will display anagrams for that text.
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